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Probability Density Transitions in the FitzHugh-Nagumo Model with Lévy Noise

Xu Yong1,2, Feng Jing1, Xu Wei1, Gu Rencai1
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China.
Corresponding author.

Computer Modeling in Engineering & Sciences 2015, 106(5), 309-322. https://doi.org/10.3970/cmes.2015.106.309

Abstract

In this paper, bifurcation analysis and numerical simulations are performed on the FitzHugh-Nagumo system in the presence of Lévy stable noise. The stationary probability density functions are obtained to examine the influences of noise intensity and stability index. Results show that under the influences of noise intensity and stability index, the dynamic of the FitzHugh-Nagumo model can be well characterized through the concept of stochastic bifurcation, consisting in qualitative changes of the stationary probability distribution. Then, the mean passage time between the resting and action state is investigated as functions of noise intensity and stability index of the external signal by means of numerical simulations. Dependences of the results on the parameters of Lévy noise are discussed to find the different mechanisms compared with Gaussian case.

Keywords

Lévy noise, FitzHugh-Nagumo model, firing time, stochastic bifurcation, stationary probability density, mean first passage time.

Cite This Article

Yong, X., Jing, F., Wei, X., Rencai, G. (2015). Probability Density Transitions in the FitzHugh-Nagumo Model with Lévy Noise. CMES-Computer Modeling in Engineering & Sciences, 106(5), 309–322.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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